Graver's optimality conditions based on Hilbert bases apply to an integer program with linear equations and a linear objective function. We generalize this result to include a fairly large class of nonlinear objective functions. Our extension provides in particular a link between the superadditivity of the difference-objective function and the Hilbert bases of conic subpartitions of ℝn. © 2003 Elsevier B.V. All rights reserved.
Murota, K., Saito, H., & Weismantel, R. (2004). Optimality criterion for a class of nonlinear integer programs. Operations Research Letters, 32(5), 468–472. https://doi.org/10.1016/j.orl.2003.11.007